1. Field of the Invention
The invention, in general, relates to a method of defining deviations of the position of pixels of at least one image recording matrix from a desired position. More particularly, the invention relates to defining such deviations of the position of pixels which are not taken into consideration during calibration of a 3-D measuring system. Where the desired position is known, the absolute position of the pixels can be defined on the basis of the deviation of the pixels from their desired position.
As used herein, “image recording matrix” connotes an arrangement capable of recording light intensity distributed over a surface and for reproducing it as a matrix. Examples of such arrangements are CCD sensors as well as CMOS sensors provided in cameras. Individual elements of the matrix are labeled “pixel”. The “position of a pixel” will be referred to as “pixel site”, the position of the pixel being defined by the center of the pixel. In an ideal image recording matrix the pixel sites are arranged in an ideal raster at a constant raster width. The pixel sites of such ideal image recording matrix are ideal pixel sites; their position will be termed “desired position”.
2. The Prior Art
For taking into consideration deviations of the real or actual pixel raster from an ideal pixel raster it has been known to measure a reference measurement. For instance, the distance between two points may be measured by defining the centers of both points. Several pixels will have an impact in defining each center. In this manner, a possible error will be averaged out. The median distance between the pixels may thus be defined with great precision, since the overall error during definition of the centers remains constant and the relative error becomes smaller at an appropriate number of pixels.
Such errors are usually taken into consideration during calibration of a 3-D measuring system (see e.g. Luhmann, T.: Nahbereichsphotogrammetrie; Wichmann Verlag, Heidelberg). However, deviations of individual pixels from the ideal pixel raster are not detected in this manner.
The signal generated by a certain pixel may be defined as follows:
  u  =            ∫      A        ⁢          MTF      ⁢                        (                      x            ,            y                    )                ·                  Φ          ⁡                      (                          x              ,              y                        )                              ⁢                          ⁢              ⅆ        x            ⁢                          ⁢              ⅆ        y            wherein μ designates the signal emitted by the pixel. MTF is the modulation transfer function as a function of the position (x,y) and φ is the light current/surface at position x,y. The integration surface A usually is larger than the surface of the pixel since electrons may diffuse across pixel borders from adjacent pixels. During mathematical processing of the signals is usually assumed that the intensity distribution corresponds to a Dirac-pulse in the center of the pixel.
A deviation of the position of the pixels of an image recording matrix from its desired position, i.e. an error in the pixel site, may be caused by several circumstances, two of which will be mentioned below:                1. The center of a pixel is shifted as a result of a deviation of the geometry of the light sensitive surface from the desired position.        2. Irregularities in the light sensitivity may cause the MTF to be non-symmetric and/or non-locally invariant. The center of gravity of the light intensity would thus be shifted as well. The effect of the deviation in the center of gravity is similar to a deviation of the geometry. The irregularity of the light sensitivity may be caused, for instance, by a deviation of the quantum efficiency.        
Obviously, the fabrication of image recording matrices (e.g. CCD sensors) is sufficiently accurate to prevent errors at the pixel site from exerting any significant effect in most applications. The literature only rarely refers to inaccuracies in pixel positions. Thus, reference is made (see Theuwissen, A. J. P.: Solid State Imaging with Charge-Coupled Devices; Kluwer Academic Publishers) that irregularities in the geometry, thickness of the layers, degree of doping or doping profile exist and that they lead to irregularities of the pixels.
These irregularities are usually classified under such labels as PSFU (photo response non-uniformity) and DSNU (dark signal non-uniformity) (see Ratledge, D.: The Art and Science of CCD Astronomy; Springer Verlag 1997). The correction of PSFU and DSNU are known in the prior art. Indeed, integration of such correction is standard in some cameras.
Also, methods are known in which information about the real position of the pixels of an image recording matrix is important. This relates to methods of optical 3-D measurement by means of cameras. In such applications, even small deviations of the pixel site may lead to relevant errors in the calculated 3-D data. A special method in which errors in the calculated 3-D data is caused by errors of the pixel sites is the subject of German patent application DE 196 23 172 C1.
Scanning the image recording matrix by a laser is one way of defining the pixel sites. For each point scanned by the laser it is possible to define the light sensitivity at this point and the pixel to which the point is associated. Hence, it is possible to define the MTF for each pixel.
However, the financial and technical outlay for equipment for laser scanning of image recording matrices necessary for 3-D measurements by cameras is too high for many users.